Table Of ContentRADIATION
EXCHANGE
An Introduction
Jack H. Taylor
Department of Physics
Rhodes College
Memphis, Tennessee
ACADEMIC PRESS, INC.
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Library of Congress Cataloging-in-Publication Data
Taylor, Jack H.
Radiation exchange : an introduction / Jack H. Taylor.
p. cm.
ISBN 0-12-684560-3
1. Electromagnetic radiation. I. Title.
QC661.T35 1990
539.2 - dc20 89-46137
CIP
Printed in the United States of America
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Preface
This book is about electromagnetic radiation. It deals with the
radiation laws, with the phenomenon of radiation exchange and
with the quantification of radiation. It can be used as a supple
ment to an introductory physics or introductory astronomy text
and also as a guide for those members of the infrared community
who would like additional insight in the area of radiation ex
change. The concepts discussed herein are well within the grasp
of undergraduate students.
It is quite possible that some of the concepts discussed in this
book are going to be unfamiliar. For example, it might be diffi
cult for the reader to accept the fact that he, or she, is radiating
electromagnetic energy. If one is radiating, then everything is ra
diating and this radiation is a form of energy. What this means
is that everything is radiating as well as receiving radiation and
if one is going to keep up with the various net energies involved
in these interactions the situation can become quite complicated.
In this book the reader is shown how to come to grips with these
interactions and how to demonstrate the phenomenon of radia
tion exchange along with many other related phenomena.
It is unfortunate that the topics discussed in this book are not
covered more thoroughly in introductory physics texts than they
are. The material covered herein forms the basis for the study
of many exciting phenomena including such things as remote
sampling, astrophysical studies, satellite studies, industrial stud
ies, etc. The decoding of messages carried by electromagnetic
radiation in remote sampling studies is a powerful investigative
ix
χ PREFACE
technique. I have always been in favor of getting undergraduates
exposed to these concepts as soon as possible in their careers.
These concepts open up many possibilities to them for directed
inquiry projects, for honors projects and for many opportunities
to involve them in meaningful experimental work in which the
theory is not more than they can handle.
Having exposed undergraduates to material such as this for
about three decades I can attest to the fact a meaningful research
involvement is a very effective way to capture and to hold one's
attention to physics. If the opportunity presents itself there is
nothing like an experiment carried out on the solar atmosphere
during a total solar eclipse to really fire up someone. A very
important spin-off resulting from such an experience as this, or
what might be called a field trip experiment, is that it forces one
to become involved with the Earth's atmosphere. Electromag
netic radiation can be modified on passing through the Earth's
atmosphere by the phenomena of scattering, refraction and ab
sorption. If only we could approach the ability to observe atmo
spheric phenomena, and then to be able to beautifully describe
the observations, as was done by the late M. Minnaert! [The
Nature of Light and Colour in the Open Air, Dover Publications,
Inc., 1954)
The style of living in the twentieth century has not been very
conducive to observation of the atmosphere and skies. Many
readers probably have never had the opportunity of seeing the
celestial sphere down to the horizon, or, for that matter, have
never seen the horizon. Many readers probably do not have
enough open space where they live to be able to have an ap
preciation of what is meant by daylight visual range. Many of
them have never seen the green flash or other setting Sun phe
nomena. Perhaps there are many who do not appreciate the fact
that the color of the zenith twilight sky is profoundly influenced
by ozone, i.e., during twilight if there were no ozone the zenith
sky would become straw yellow in color as twilight progressed.
The late E. O. Hulburt has pointed out that ozone, by means of
its weak Chappius absorption band in the yellow, keeps the sky
PREFACE xi
blue during twilight. We must all constantly force ourselves to
be aware of atmospheric phenomena. In the process we are going
to learn much about optical physics.
There are many problems that one needs help with in study
ing electromagnetic radiation that has traversed long atmospheric
paths. For one thing, someone will look at a light source in the
laboratory and note that it is rock stable and assume that the
same will be true if they should look at a source outside the lab
oratory that is far away. Another problem is that most people
think visible, i.e., they think that all electromagnetic radiation is
in the visible spectrum. It is easy to understand why they think
like this but it is imperative that this habit be broken, and the
sooner the better.
As a teacher it is a constant battle for me to try to drive home
the fact that the piece of the spectrum that one can see is an
unbelievably small piece of the entire electromagnetic spectrum.
Another problem that most people need help with is the fact
that the Earth's atmosphere is not free of absorption when one
considers the infrared portion of the spectrum. For example,
a person might note that someone has on a white shirt. This
person will also note that when the wearer of the white shirt
begins to walk away from him (or her) that the shirt continues to
look white and will infer from this that the Earth's atmosphere
is free of absorption because the color of the white shirt does
not change as it gets farther away. This error in reasoning is
brought about because one is thinking visible. It is imperative to
appreciate the fact that if our eyes could detect infrared radiation
then indeed the color of the white shirt would change as more
and more of the light scattered off the shirt is absorbed by the
Earth's atmospheric path.
This book is also concerned with the quantification of elec
tromagnetic radiation, i.e., the measurement of wavelengths and
the measurement of the intensity of the radiation (i.e., how much
radiation there is.) In discussing the quantification of radiation
it will be the details of measuring intensity that will be our chief
xii PREFACE
concern. In addition, the chief emphasis of this book is on the in
frared region of the spectrum. There are several reasons for this
emphasis on the infrared. First, it is in the infrared region of
the electromagnetic spectrum that so many physical phenomena
can be interestingly demonstrated. Secondly, it is the spectral
region where the radiation laws can be pedagogically presented.
Thirdly, it is difficult to carry out quantitative measurements in
the infrared and operation in this region of the spectrum has
been compared to carrying out measurements in a sea of radia
tion where all objects are radiating and exchanging energy with
each other.
Many possible research projects, other than eclipse studies,
will no doubt come to mind as you read and study this book.
Some that immediately come to mind are the measurement of the
solar constant, the measurement of the effective radiating tem
perature of the ozonosphere lying above the Earth, radiometric
and spectroscopic studies of lightning, spectral radiant emittance
studies of the radiation from carbon arcs, radiation exchange be
tween Earth and space and other similar experiments. It should
be pointed out that radiometry offers an excellent opportunity
to introduce the study of systems analysis.
After studying this book it is to be hoped that the reader will
have developed a better feeling for the phenomenon of radiation
exchange and will appreciate its importance in the scheme of
things in nature.
The material contained in this book is based on a series of
articles published by the Optical Society Of America in Applied
Optics and Optics News. The article in Applied Optics was pub
lished in February, 1987, and the articles in Optics News were
published approximately monthly from January, 1987, to Decem
ber, 1987. The Optical Society has graciously granted permission
for the republication of the material in its present form.
Chapter 1
Radiation Exchange
1 · 1 Intro duet ion
It has been my observation that most texts provide a minimal
coverage of the phenomenon of radiation exchange. What lit
tle material there is on radiation exchange in most introductory
texts is usually covered in the section dealing with heat, in partic
ular, in the section dealing with the transfer of heat by radiation.
In fact, radiation exchange is not listed in the indices of the most
frequently used texts for physics majors in this country. The au
thor has found this to be an area of considerable interest to most
people.
It is important to have some understanding of the key ideas
involved in radiation exchange. Understanding and appreciating
radiation exchange is necessary for effective work in infrared ra-
diometry. Radiation exchange is an area of physics where one can
use, and needs, as much help from the textbook as possible. Phe
nomena involving radiation exchange are everywhere; one simply
needs help in recognizing them. The subject of radiation ex
change, being extremely open-ended, holds great possibilities for
the reader. You will find that it is laden with astrophysical and
space applications, both of which interest most people. Depend
ing on the extent to which one develops this area, it has been my
3
4 CHAPTER I. RADIATION EXCHANGE
experience that many ideas and suggestions for student exper
iments, directed inquiries, and honors projects are quite likely
to arise. In this connection, let me say that I routinely have
my students measure the effective radiating temperature of the
ozonosphere above Memphis.
1.2 Everything Is Radiating
1.2.1 Stefan-Boltzmann Law
A good place to start a discussion of radiation exchange is with
the Stefan-Boltzmann Law. Most texts write the law as
Η = ΑεσΤ4 (1.1)
and state that this gives the rate of radiation of energy from a
surface of area A and absolute temperature Γ and that e (the
radiant emissivity) is a dimensionless number between 0 and 1.
The quantity σ is the Stefan-Boltzmann constant. This law was
first arrived at empirically. The theoretical basis on which it rests
is the Plank Radiation Law, which is discussed in Chapter 3.
Solving the above equation for H/A one obtains the units of
watts/area. This is where most texts leave the units of Equa
tion (1.1). They fail to point out that the units of H/A are
really watts/area radiated into a hemisphere. This failure to em
phasize that this is indeed radiation into a hemisphere can be
quite frustrating to someone who is trying to calculate the power
from a radiating object that is intercepted by a mirror, using
only what most introductory texts state as being the units of
Equation (1.1).
Throughout this book, we shall be talking about solid angles
(i.e., about steradians). Figure 1.1 is a sketch showing the defini
tion of both a plane angle and a solid angle. Since dQ = dA/R 2,
one determines the solid angle surrounding a point, Ω, by inte
grating over the entire sphere to obtain 4KR 2/R2 = 4π. In other
1.2. EVERYTHING IS RADIATING 5
dQ = dj| STERADIAN
W (b)
Figure 1.1: A review of angles, (a) A two-dimensional (or plane)
angle, (b) A three-dimensional (or solid) angle. Steradian comes from
the Greek word stereos, meaning solid.
words, there are 4π steradians surrounding a point.
Since we are talking about radiation into a hemisphere, one
might easily reason that Η/Α/2π would have the units of
watts/area/steradian. The units are correct, but we should have
divided by π and not 2π for reasons that are to be discussed
shortly.
In present-day radiometric terminology a quantity with the
units of watts/unit area/steradian is called the radiance and is a
useful concept in radiometry.
Equation (1.1) contains many of the key ideas of radiation
exchange. It clearly shows that all objects that have a tem
perature radiate, and since one cannot achieve absolute zero, it
means that all objects are radiating. An understanding of this
important equation will come with continued use and study.
6 CHAPTER l. RADIATION EXCHANGE
Figure 1.2: Development of the concept of radiance.
1.2.2 Development of the Concept
of Radiance
Suppose we are interested in the amount of power radiated per
unit area into a steradian normal to the radiating surface as
shown in Figure 1.2(a).
The idea of a point source radiating uniformly in all direc
tions is a useful concept theoretically but one that is difficult to
achieve in practice. For the majority of cases encountered, the
source will be what is termed an extended source, that is, it will
have a measurable area and must be treated differently than a
point source. For a point source we could characterize it quite
adequately by stating the number of watts per steradian radiated
in a given direction. For an extended source we could character
ize it by stating the number of watts per unit area per steradian
radiated normal to the surface.
